Name:_______________________________ Date:____________ Hour:______ Chapter 5:
Solving Systems of Equations
5.1 Solving Systems of Linear Equations by Graphing
Standards
8.EE.8a
8.EE.8b
8.EE.8c
Learning Objectives (I can…)
 Write and solve systems of linear equations by graphing.
 Solve real-life problems
A __________________________________________________ is a set of __________ or more linear equations
in the same variables. An example is shown below.
A _______________________ of a system of linear equations in two variables is an
____________________________ that is a solution of each equation in the system. The solution of a
system of linear equations is the point of _________________________ of the graphs of the
equations.
Key Idea
Solving a System of Linear Equations by Graphing
Step 1:
Step 2:
Step 3:
Name:_______________________________ Date:____________ Hour:______ Chapter 5:
Solving Systems of Equations
Example 1: Solving a System of Linear Equations by Graphing
Solve the system by graphing.
Step 1:
Step 2:
Step 3:
On Your Own: Solve the system of linear equations by graphing.
1.
2.
Name:_______________________________ Date:____________ Hour:______ Chapter 5:
Solving Systems of Equations
Example 2: Real-Life Application
A kicker on a football team scores 1 point for making an extra point and 3 points for
making a field goal. The kicker makes a total of 8 extra points and field goals in a
game and scores 12 points. Write and solve a system of linear equations to find the
number x of extra points and the number y of field goals.
On Your Own: Solve the system of linear equations by graphing.
3.
4.
Name:_______________________________ Date:____________ Hour:______ Chapter 5:
Solving Systems of Equations
5.2 Solving Systems of Linear Equations by
Substitution
Standards
8.EE.8b
8.EE.8c
Learning Objectives (I can…)
 Write and solve systems of linear equations by substitution.
 Solve real-life problems.
Key Idea
Solving a System of Linear Equations by Substitution
Step 1:
Step 2:
Step 3:
Example 1: Solving a System of Linear Equations by Substitution
Solve the system by substitution.
Name:_______________________________ Date:____________ Hour:______ Chapter 5:
Solving Systems of Equations
On Your Own: Solve the system of linear equations by substitution. Check your
solution.
Example 2: Real-Life Application
You buy a total of 50 turkey burgers and veggie burgers for $90. You pay $2 per
turkey burger and $1.50 per veggie burger. Write and solve a system of linear
equations to find the number x of turkey burgers and the number y of veggie burgers
you buy.
Name:_______________________________ Date:____________ Hour:______ Chapter 5:
Solving Systems of Equations
On Your Own:
4. A juice stand sells lemonade for $2 per cup and orange juice for $3 per
cup. The juice stand sells a total of 100 cups of juice for $240. Write and
solve a system of linear equations to find the number of cups of
lemonade and the number of cups of orange juice sold.
Name:_______________________________ Date:____________ Hour:______ Chapter 5:
Solving Systems of Equations
5.3 Solving Systems of Linear Equations by
Elimination
Standards
8.EE.8b
8.EE.8c
Learning Objectives (I can…)
 Write and solve systems of linear equations by elimination.
 Solve real-life problems.
Key Idea
Solving a System of Linear Equations by Elimination
Step 1:
Step 2:
Step 3:
Step 4:
Example 1: Solving a System of Linear Equations by Elimination
Solve the system by elimination.
Name:_______________________________ Date:____________ Hour:______ Chapter 5:
Solving Systems of Equations
On Your Own: Solve the system of linear equations by elimination. Check your
solution.
Example 2: Solving a System of Linear Equations by Elimination
Solve the system by elimination.
Name:_______________________________ Date:____________ Hour:______ Chapter 5:
Solving Systems of Equations
On Your Own: Solve the system of linear equations by elimination. Check your
solution.
Example 3: Real-Life Application
You buy 8 hostas and 15 daylilies for $193. Your friend buys 3 hostas and 12 daylilies
for $117. Write and solve a system of linear equations to find the cost of each daylily.
Name:_______________________________ Date:____________ Hour:______ Chapter 5:
Solving Systems of Equations
Summary:
Name:_______________________________ Date:____________ Hour:______ Chapter 5:
Solving Systems of Equations
5.4 Solving Special Systems of Linear Equations
Standards
8.EE.8a
8.EE.8b
8.EE.8c
Learning Objectives (I can…)
 Solve systems of linear equations having no solution or infinitely
many solutions.
Key Idea
Solutions of Systems of Linear Equations
A system of linear equations can have _________________________, _______________________, or
________________________________________________.
Example 1: Solving a System: No Solution
Solve the system.
Name:_______________________________ Date:____________ Hour:______ Chapter 5:
Solving Systems of Equations
On Your Own: Solve the system of linear equations. Check your solution.
Example 2: Solving a System: Infinitely Many Solutions
The perimeter of the rectangle is 36 units. The perimeter of the triangle is 108 units.
Write and solve a system of linear equations to find the values of x and y.
Name:_______________________________ Date:____________ Hour:______ Chapter 5:
Solving Systems of Equations
On Your Own: Solve the system of linear equations. Check your solution.